The importance of prime numbers in physical theories

Question

Imagine that a friend asks me about what is the importance of prime numbers in physics. What should I tell him/her?

I know that natural numbers should be important in quantum mechanics because there are some quantized quantities. But are prime numbers useful in any branch of physics? It is obvious that multiplication and division are important in physics but it is about real/rational numbers.

Question. Can you provide idea about what is the importance of prime numbers in physics? I'm interested in theories, not in a specific application from a branch of physics. You can add examples or well your reasoning about why prime numbers aren't important in theoretical physics. I wish you a good day.

Answer 1

In addition to @Keith's comment (or should I say a clone of it), a Google search on: prime numbers in physics yielded me the following results:

• Link 1

• Link 2

• Link 3

and many more.

Also see this interesting paper by Marek Wolf.

Answer 2

Theoretical physicists are modelling how some things "in nature", by their opinion, are functioning. They seek for laws that govern "natural phenomena" and they try to present them in mathematical form.

In that process they use known mathematical theories if those theories are advanced enough to suit their needs and they sometimes advance those theories by their engagement in the whole process.

From all the branches of mathematics the theory of numbers is, in my opinion, the most non-physical one.

But, of course that sometimes connections with some models of physics and theory of numbers arise and become apparent, because also the theory of numbers is connected to other areas of mathematics.

So , it is expectable to see some parts of the theory of numbers to appear in physics, but at the present time there is not much of them, or at least I do not know aboot much of them.